TRANSFORMATION OF A STAR TO DELTA FOR NETWORK RELIABILITY CALCULATIONS

It is shown that transformation of a star to delta is possible under certain conditions. Expressions are derived for the probabilities of elements of an equivalent delta given the probabilities of elements of star. All nodes are assumed to be perfect. It is also assumed that two nodes of star / delta are such that both have inflow only or both have outflow only with respect to the remaining network. It is shown that the nonlinear equations have closed form solution. The values of the variables are real numbers and satisfy the usual properties of probability. i.e., they lie between zero and one. A simple modification is suggested to use this analysis even when the star has an imperfect centre node.